Invariant factors, Julia equivalences, and the (abstract) Mandelbrot set / Karsten Keller
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1732Langue : anglais.Éditeur : Berlin : Springer, 2000ISBN: 9783540674344.ISSN: 1617-9692.Sujet MSC : 37Fxx, Dynamical systems and ergodic theory - Dynamical systems over complex numbers37F10, Dynamical systems over complex numbers, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F46, Dynamical systems over complex numbers, Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets
37F50, Dynamical systems over complex numbers, Small divisors, rotation domains and linearization in holomorphic dynamics
37F20, Dynamical systems over complex numbers, Combinatorics and topology in relation with holomorphic dynamical systemsEn-ligne : Springerlink | Zentralblatt | MathSciNet
This volume is a detailed study of the dynamics of quadratic polynomials from the point of view of symbolic or topological dynamics. It is based on Thurston’s theory of quadratic laminations, which give topological models for Julia sets of quadratic polynomials, based on combinatorial data; this theory also gives a model for the Mandelbrot set called ‘quadratic minor lamination’. The present volume extends these concepts to give a self-contained study of a topological model of Julia sets and of the Mandelbrot set (which are homeomorphic models for locally connected compact sets). Many combinatorial properties of the Mandelbrot set, and many properties of quadratic symbolic dynamics are derived in this model. (Zentralblatt)
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